Light Subgraphs in the Family of 1-Planar Graphs with High Minimum Degree

作     者：Xin ZHANG Gui Zhen LIU Jian Liang WU 

作者机构：School of MathematicsShandong University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第6期

页      面：1155-1168页

核心收录：

学科分类：0303[法学-社会学] 03[法学] 030303[法学-人类学] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10971121, 11026184, 61070230) Research Fund for the Doctoral Program of Higher Education (Grant No. 20100131120017) Graduate Independent Innovation Foundation of Shandong University (Grant No. yzc10040) the financial support from the Chinese Ministry of Education Prize for Academic Doctoral Fellows 

主　　题：1-Planar graph lightness height discharging 

摘      要：A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, it is shown that each 1-planar graph with minimum degree 7 contains a copy of K2 V （K1 ∪ K2） with all vertices of degree at most 12. In addition, we also prove the existence of a graph K1 V （K1∪K2） with relatively small degree vertices in 1-planar graphs with minimum degree at least 6.